A:AnswerYes. Xbox controller compatibility is native to Windows 10 provided you have that, likely earlier versions as well. Just install and pair in PC settings bluetooth devices, and off you will go. It might lose your pairing with the Xbox itself and you would need to re-pair to use there.
A:AnswerThis unit is intended for use with Windows 10 or Linux based PCs. It is not directly compatible with a cell phone via a USB adapter. https://www.asus.com/us/Networking/USB-BT500/specifications/
A:AnswerYes, that product appears to support PC Bluetooth pairing. https://support.apple.com/en-us/HT209544
Please verify that your PC is running either Windows 10 or Linux, and you shouldn't have any issues.